In bowl, whisk cocoa powder and cornstarch; whisk in 1 1⁄2 cups of the half and half. In saucepan, heat remaining 1 cup half and half and the sugar over medium heat, stirring, until sugar is dissolved. Whisk in cocoa mixture and melted chocolate. Cook, stirring, until filling begins to bubble; continue to cook, whisking, until very thick, about 2 minutes longer. Off heat, whisk in butter and vanilla.